For the channel model, firstly we consider a large-scale fading model according to [1]}, where the BS-RIS-user link suffers the “double-fading effect” discussed in [2]}. Therefore, let \(d_{\rm Bu}\) , \(d_{\rm BR}\) , \(d_{\rm Ru}\)  denote the distance between bs and user, bs and ris, ris and user, respectively, the distance-dependent path loss of the BS-user link can be written as
\(\begin{aligned}{f_{\rm d}}({d_{\rm Bu}}) = {C_{\rm d}}{G _{\rm B}}{G _{\rm u}}{d_{\rm Bu}}^{ - {\kappa _{\rm Bu}}},\end{aligned}\) 
